Angle of arrival (AoA) measurement is a method for determining the direction of propagation of a radio-frequency wave incident on an antenna array. AoA determines the direction of the transmitted signal and may be determined by measuring the difference in received phase at each element in an antenna array.
FIG. 1 depicts a two element array. Antenna A 10, and antenna B 11, are spaced apart by a distance D. An incoming RF wave 12 (shown as RF signals 12a and 12b) is received at antenna A 10, and at antenna B 11. The incoming RF wave 12 is arriving at an angle θ 14 incident to the plane of the two antennas 10 and 11. The RF signal 12b received at antenna B 11 has travelled further than the RF signal 12a received at antenna A 10 by a distance d 15.
The extra distance travelled by the RF signal, d, is related to the distance between the antennas, D, and the angle of the arrival of the RF signal, θ; using simple geometry:d=D cos θ  (1)                The phase difference φ between the RF signal received at antenna B 11 and the RF signal received at antenna A 10 is:φ=d/2πλ where λ is the wavelength of the RF signal.  (2)Hence, φ=D cos θ/2πλcos θ=φ·2πλ/D or θ=a cos(φ·2πλ/D)  (3)        
The phase difference φ between the two RF signals received at each of the antennas is therefore related to the angle of arrival θ of the RF signal. For example, if the RF signal is coming from a direction directly in front of the two antennas then φ=0 and θ=90° or π/2 radians.
A common method to measure the phase difference φ is to add the signals from both antennas as depicted in FIG. 2. The output from each antenna 10 and 11 is connected to the inputs of an RF adder 21 which provides the sum of the two signals 22 at its output.
If the received signals at antennas 10 and 11 have amplitude A, then the output 22 of the RF adder 21, using simple trigonometry, is:Sum=A√{square root over (2+2 cos Ø)}  (4)
If the distance D between the antennas 10 and 11 is arranged to be half a wavelength, D=λ/2, then when the RF signal is coming from a direction from the side of the antennas, θ=0, the two RF signals from the two antennas will be in anti-phase and will cancel out and the result of the summation will be an RF signal of zero amplitude. When the RF signal is coming from the front of the two antennas, θ=π/2, then the two RF signals will add in phase and the result of the summation will be an RF signal at the maximum amplitude. FIG. 3 shows a graphical representation 30 of the amplitude of the RF signal 22 at the output of the RF adder 21 as the angle of arrival varies from 0 to 180 degrees.
FIG. 4 shows a graphical representation 40 of the amplitude of the RF sum signal 22 at the output of the RF sum block 21 plotted against angle of arrival as the angle of arrival varies from 0 to 180 degrees and when the distance D between the antennas 10 and 11 is set to one wavelength, D=λ. Note that the amplitude is at a maximum at angles of arrival 0, 90 and 180 degrees, and at a minimum at angles of arrival 60 and 120 degrees.
A common method to measure the angle of arrival is to rotate the two antennas around their axis such that the sum of the received signals is at a maximum and hence the direction of the incident wave is known. The accuracy of this approach can be increased by using two directional antennas or by increasing the distance between the two antennas which results in a narrower front beam width but also more than one maximum. A disadvantage of this approach is that the antenna assembly needs to be rotated, the accuracy is limited by the directionality of the individual antennas. Also, increasing the directionality of the antenna necessitates that the size of each antenna increases. For example, the beam width of an antenna is related to the gain of the antenna; the narrower the beam width, the higher the gain. For example a patch antenna consists of a flat rectangular sheer or “patch” of metal, mounted over a larger sheet of metal called a ground plane. An example of a patch antenna at 2.4 GHz has a gain of about 8 dBi, a 3 dB beam width of about 60 degrees and has side lengths of about 4 inches. An array of 4 patch antennas, side by side, would be in the order of 12 to 16 inches in length and would have a horizontal beam width of about 20 degrees. Achieving a narrow beam width in the order of approximately 5 degrees requires a linear array of 16 patch antennas. This antenna array could have a length of about 64 inches.